We introduce the concept of mixture inner product spaces associated with a given separable Hilbert space, which feature an infinite-dimensional mixture of finite-dimensional vector spaces and are dense in the underlying Hilbert space. Any Hilbert valued random element can be arbitrarily closely approximated by mixture inner product space valued random elements. While this concept can be applied...

This paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   The main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...

In this paper, we present the Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) goodness of fit statistics for stationary and non-stationary random fields. Namely, we adopt an easy-to-apply method based on a random projection of a Hilbert-valued random field onto the real line R, and then, applying the well-known AD and KS goodness of fit tests. We conclude this paper by studying the behavior o...

For an arbitrary Hilbert space-valued Ornstein-Uhlenbeck process we construct the Ornstein-Uhlenbeck Bridge connecting a starting point x and an endpoint y that belongs to a certain linear subspace of full measure. We derive also a stochastic evolution equation satisfied by the OU Bridge and study its basic properties. The OU Bridge is then used to investigate the Markov transition semigroup as...

In this article, we introduced an iterative scheme for finding a common element of the set of fixed points of a multi-valued hemicontractive-type mapping, the set of common solutions of a finite family of split equilibrium problems and the set of common solutions of a finite family of variational inequality problems in real Hilbert spaces. Moreover, the sequence generated by the proposed algori...

For an arbitrary Hilbert space-valued Ornstein-Uhlenbeck process we construct the Ornstein-Uhlenbeck Bridge connecting a given starting point x and an endpoint y provided y belongs to a certain linear subspace of full measure. We derive also a stochastic evolution equation satisfied by the OU Bridge and study its basic properties. The OU Bridge is then used to investigate the Markov transition ...

Vector-valued L p-convergence of orthogonal series and Lagrange interpolation. Abstract We give necessary and sufficient conditions for interpolation inequalities of the type considered by Marcinkiewicz and Zygmund to be true in the case of Banach space-valued polynomials and Jacobi weights and nodes. We also study the vector-valued expansion problem of L p-functions in terms of Jacobi polynomi...